21st Century Fox Inc. rejected an acquisition offer for its entertainment assets from cable giant Comcast Corp. largely over antitrust concerns, a regulatory filing said, even though the bid was 16% higher on a per-share basis than what Walt Disney Co. ultimately agreed to pay.

After extended discussions, Fox’s board decided that Comcast’s offer was too risky to accept, according to the filing. Fox was concerned such a deal might not pass muster in Washington, and even if it did, it would require divestiture of valuable...